Endogenous Flip Clocks from Anisotropic Local Memory in a Self-Interacting Lattice Walker

This note studies a self-interacting lattice walker with anisotropic local memory. At each step, the walker forms a local decision field from accumulated wake and ambient forcing, selects a cardinal move by a cost-normalized score with explicit turning cost, and then deposits an oriented asymmetric body-frame stencil at the newly occupied site. The deposited stencil spreads by a discrete convolutional rule and becomes part of the wake field for later steps. In the ambient-off regime, this minimal rule set generates a compact endogenous flip clock: after a fixed onset step, the walker undergoes sharply regular reversals whose period is controlled by a lag parameter applied to stencil orientation. Across the tested sweep τ = 0, …, 12, the inter-flip coefficient of variation is zero at every sampled value. With ambient stochastic forcing enabled, the same mechanism persists in broadened exploratory regimes, where lag no longer acts as a simple period dial but instead modulates flip activity, spatial extent, and chirality-related statistics. Null models and ablations isolate the roles of wake memory, anisotropic deposition, spread geometry, heading–wake coupling, and cost-normalized local selection. The result is a compact mechanistic example of endogenous clocking and structured local-memory dynamics on a lattice.